The treatment of Heisenberg films with many-body Green's function theory
(GFT) is reviewed. The basic equations of GFT are derived in sufficient detail
so that the rest of the paper can be understood without having to consult
further literature. The main part of the paper is concerned with applications
of the formalism to ferromagnetic, antiferromagnetic and coupled
ferromagnetic-antiferromagnetic Heisenberg films based on a generalized
Tyablikov (RPA) decoupling of the exchange interaction and exchange anisotropy
terms and an Anderson-Callen decoupling for a weak single-ion anisotropy. We
not only give a consistent description of our own work but also refer
extensively to related investigations. We discuss in particular the
reorientation of the magnetization as a function of the temperature and film
thickness. If the single-ion anisotropy is strong, it can be treated exactly by
going to higher-order Green's functions. We also discuss the extension of the
theory beyond RPA. Finally the limitations of GFT is pointed out.Comment: 124 pages, 32 figures, accepted by Physics Report
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